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Artificial gravity meeting zero gravity

  1. Aug 25, 2010 #1
    A little puzzle that's been in my mind for a while and I figured I would ask, in case someone a little more knowledgeable could shed some light on it.

    Assuming one had a spaceship formed by two "hoops," one inside the other. If one of the hoops rotated at a velocity high enough to provide a sense of artificial gravity, and the other hoop remained stationary. A ladder or stairway would provide access between each hoops from the inside. If someone was inside the moving hoop, with gravity and all, then went into the stationary hoop, what would happen?

    I'm assuming this would take place in a low gravity environment. However, I'm wondering if the individual would start floating as he made his or her way down, or right at the moment they stepped off the ladder? Would someone in the stationary hoop floating right over the stairway suddenly crash on it as it moved under him?

    Here's a not so good drawing, if it helps any.
    [PLAIN]http://img203.imageshack.us/img203/6279/stairship.png [Broken]

    Thanks!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 25, 2010 #2

    russ_watters

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    Which is stationary and which is rotating?
     
  4. Aug 25, 2010 #3

    DaveC426913

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    The first thing you need to recognize is that there is no artificial gravity in a spinning space station. All there is is inertia - moving in a straight line, tangential to the perimeter of the hoop.

    That movement comes from the occupant having been given a push by touching a surface moving relative to him (or air resistance).

    No touch = no push
    No push = no tangential movement
    No tangential movement = no artificial gravity

    In summary, the occupant will be weightless until
    1] he physically touches a surface moving relative to him imparting some tangential movement
    AND THEN
    2] his tangential movement subsequently causes him to bump into the wall again. It is THIS motion-and-bump that he experiences as an apparent force pulling him to the floor.


    He can float weightless next to a space station floor whizzing by at 100mph forever. It is when he reaches out and makes contact with the wall (causing him to pick up some motion relative to the space station as a whole) that he begins to experience artificial gravity. And the strength of the AG wil be proportional to how much motion he picks up. Just grazing it with his fingers won't do much - at first, but it's enough that he will slowly and inevitably speed up and come to rest moving at 100mph.
     
    Last edited: Aug 25, 2010
  5. Aug 26, 2010 #4
    Most of him will.
    There'd probably be a few gobs and splatters floating around.
     
  6. Aug 26, 2010 #5
    That actually makes a lot of sense, thanks for the clarification!
     
  7. Aug 26, 2010 #6
    interesting. So if the person is moving at 100mph on the outer wall of the space station, how do they return to weightlessness relative to the moving floor? If they accelerate to 100mph in the opposite direction as the outer wall, they become weightless? What if they accelerate to 100mph in the same direction the wall is moving? Do they become heavier (i.e. gain more momentum)?

    So, if I understand this right and there was a very large hollow cylindrical space station, a person wanting to travel hundreds of miles would just need to accelerate to the speed of the station's momentum from the ground and could then fly without gravity to the other side where it would have to accelerate up to speed again to land?
     
  8. Aug 26, 2010 #7

    DaveC426913

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    Yes on both.

    One of the (many) tricky things about AG rotating spaces tations is that moving to spinward will make you feel heavier and moving to antispinward will make you lighter. Move too fast to antispinward and you will become so light that you will have difficulty getting traction, you'll go more "up" than "along".

    Well, yes. It's not quite as simple as that, but yes.

    For one, air will be moving along with the rotation, and will work to keep you moving along with the station. At its worst, you'd be battling a 100mph wind to keep weightless, so...
     
  9. Aug 26, 2010 #8
    So as you're accelerating in the antispin direction, your weight is approaching zero while your lift is increasing toward whatever it would be at 100mph. At some point in between 0 and 100mph, you would reach some kind of ideal combination of lift and weight and would take off stably, right? Then could you fly more or less straight up (into the headwind) toward your destination and just glide with the wind back to a reasonable landing speed?

    I think I'm just saying what you did in a wordier way, but I wonder how the reduced weight would interact with the lift and what kind of trajectory the plane would have to take.
     
  10. Aug 26, 2010 #9

    DaveC426913

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    There's no lift. All there is is you trying to run and resulting in pushing off the ground.


    Note that you cannot run at 100mph. To achieve weightless, you'll need to be in a space staiton whose rotational speed does not exceed your running speed.
     
  11. Aug 27, 2010 #10
    In my example the space station was hundreds of miles across and there was a plane accelerating in the anti-spin direction simultaneously losing weight and gaining lift. In your example, the space station seems to be smaller and slow enough to achieve weightlessness on foot. I was interested in the dynamics of lift vs. weight in a plane flying counter the spin direction.
     
  12. Aug 27, 2010 #11

    DaveC426913

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    Right. I saw that after-the-fact.

    But you're looking at the least interesting case. You're still building a large plane that has to accelerate to 100mph and use lifting surface to get off the ground. Why not take advantage of the unique quirks of the AG? It's much more fun.

    In a nutshell, in a large enough space station, your airplane would take off just like a plane on a planet would, but would experience an excess of lift (lift it would not need). In fact, the lift would have to be coutnered by control surfaces to get the plane to fly straight instead of rising too rapidly.

    Moreover, the plane would now have no use for its wings (since there's no gravity force), and would become simply a propellor-powered missile, its direction of motion determined by the propellor's axis. Control surfaces would simply redirect the long-axis of the craft.
     
  13. Aug 27, 2010 #12
    I think you're assuming either 100mph and weightlessness or 0mph and full AG. What I'm looking at is where the plane accelerate anti-spinward, which decreases its weight while increasing its lift. As you said, the air inside the space station basically rotates along with the "ground" so it's not possible to go in the anti-spin direction without attaining lift. However, as you say if you achieve 100mph the plane would become weightless and turn into a propellor-powered airborne torpedo.

    So the interesting thing would be to plot a course for the plane that accelerates to, say, 50mph where it still maintains weight due to the rotation of the station, but the weight is reduced while lift is present. Then, once it is airborne would it then make sense to go ahead and accelerate to full weightlessness or should the plane operate at <100mph to remain sub-weightless?
     
  14. Aug 27, 2010 #13

    DaveC426913

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    :shrug:
    OK, I just don't see much interesting about that is all. I know how planes work. This is just more of the same.

    What I find more interesting is the longtime dream of humanity coming to life - a person flying by muscle-power alone.
     
  15. Aug 27, 2010 #14
    Ok, well how fast would the station have to be rotating to produce 1G? I'm sure you could make a space station small enough to generate 1G with relatively low speed. In that case, you could lose lots of weight by running antispinward but how would you propel yourself once you leave the ground?
     
  16. Aug 27, 2010 #15

    DaveC426913

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    Other way around.
    For 1G, slow speed requires a big station. You want a small station, speed must be high.
     
  17. Aug 27, 2010 #16
    Why are the speeds actually even different? Isn't the G-force just a product of the momentum of the objects inside the station. So shouldn't any object move with 1G of force if it is accelerating at a given rate?
     
  18. Aug 27, 2010 #17

    DaveC426913

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    The object is not accelerating. The object is travelling in a straight line (tangential to the space station's rim). It is the space station that curves up toward the object. It is this floor-coming-toward-object that is (mis)interpreted as an apparent force pulling the object toward the floor.


    Shoot, I am now no longer sure that this is correct:

    Here're some numbers:
    Properties_of_spin_graviity_%281g%29.png
     
  19. Aug 27, 2010 #18
    The force is proportional to the radius and to the square of angular velocity, but tangential velocity is directly proportional to both. If you quadruple the radius, you must halve the rotation rate, which still gives you double the linear velocity. Larger stations require lower rotation rates, but higher tangential velocities. (As the radius of curvature increases, the speed along that curve must increase to maintain the same acceleration.) And in this case, it seems to be that tangential velocity that's of interest, not the rotation rate.
     
  20. Aug 27, 2010 #19

    DaveC426913

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    Ah right. That's why it threw me. One goes up, the other down.

    Large stations are preferred because, ideally, you want the rotation rate as low as possible (less disorientation, less Coriolis Effects, etc) but you do end up with a higher tangential velocity (though the everyday occupants don't concern themselves much about that.)
     
  21. Aug 27, 2010 #20
    Does this mean that a very large space station could rotate very slowly to generate 1G of AG? Would that mean that weightlessness would be achieved with relatively little antispinward acceleration? That seems counterintuitive somehow, but only because I can't imagine my weight increasing or decreasing drastically due to small variations in speed.
     
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